I'm encouraged by your
comments. I acknowledge that
the traveling wave (TW) has become the dominant paradigm of cochlear
mechanics, but as we are beginning to see, it has definite limitations. The TW is a useful shorthand for a
description of how the cochlear partition appears to behave to an observer; the problem is that, as you say, in itself
the TW has no causal power, it is an epiphenomenon. And yet people continue to
call on the TW to do all sorts of things to stimulate hair cells. The misapprehension arises because the TW can be so
easily modeled mathematically; however, the mathematics tends to make us lose
sight of what quantities are driving which others: which parameters are
descriptions and which are causally efficacious.

Von Bekesy, in one of his later papers
with Wever and Lawrence, acknowledged that the TW could be seen as merely
descriptive of the result of the action of oscillating acoustic pressure in the cochlea.

The reason I am
promoting a resonance theory of hearing is that, as Helmholtz
appreciated, resonance allows small stimuli, through successive cycles,
to build up to have an appreciable effect. It is 'efficient', unlike the TW
theory, which requires a large mass (the cochlear partition) to move and to
carry forward its energy to successive hair cells. The problem is that we know
the ear can detect sound energy of the order of electron volts; this is not
enough energy to move the whole partition.

Our aim is therefore to have
acoustic energy 'funnelled' to individual resonators in the cochlea. The
question is, of course, what are the
resonant elements? One desirable outcome might be to have the acoustic energy
funnelled to just that one inner hair cell (in the cochlear
frequency map) that represents the
frequency concerned. But, we know from Gold that we should put the amplifier
before the detector. Everyone seems pretty sure the cochlear amplifier resides
with the active outer hair cells. So our aim should be to funnel precious
acoustic energy into the OHCs, have it amplified, and detected by the
IHCs.

How to funnel acoustic energy into OHCs? You seem to believe that
the OHC stereocilia are the resonant elements, but I find it hard to see how
that could happen. I would be interested to hear how you propose that the OHC
stereocilia are stimulated.

I consider the body of the OHC to be a much
more likely receptor of acoustic energy. Let me explain why.

My starting
point was to create a theory that could explain spontaneous otoacoustic
emissions. Here we observe sound coming out of the cochlea without any
stimulation at all. That is, the cochlear partition is just sitting there, in
the quiet of an anechoic chamber, and narrow-band signals are being produced.
This was the phenomenon that got me into hearing research, and it seemed clear
to me at the time that the TW theory,
with its large moving mass and lack of sharp tuning, was not a good candidate
for an explanation. I produced a paper for Hearing Research in 1992
(vol 58, pp 91-100) which examined the circadian and menstrual variations of
SOAEs and came to the conclusion that it was intracochlear pressure
that changed their frequency. Now, how can static pressure affect the activity of an OHC
(the candidate element)?

It seemed to me that pressure must be affecting the body of an OHC. Such
cells are under pressure, are compressible
(Zenner 1992), contain pressure sensors in their cell walls, and are seen
to respond to oscillating acoustic pressure in vivo (when a
pipette projecting an oscillating jet of water is directed at the body of an
OHC, the cell responds). Moreover, I have argued in my MSc thesis (ANU, 1998)
that the alternative explanation for pressure affecting SOAE frequency
(involving changes of mass of the partition due to blood flow changes) is not
convincing. Interestingly, early papers by Wilson
recorded that static pressure could precipitate tinnitus and labile SOAEs. Any
theory of cochlear mechanics needs to explain this susceptibility to static
pressure.

The idea that oscillating acoustic
pressure directly affects OHCs in a similar
way is attractive because it means
that acoustic energy is funneled straight to the OHCs. The OHCs are compressible elements immersed in
incompressible fluid contained within rigid bone. All the available energy therefore goes straight to the OHC (and a portion to the round window). In this
respect, it is noteworthy that OHCs are surrounded by the spaces of Nuel. To my
knowledge, every other cell in the body is placed next to its companion
cells without any other intervening space. In contrast, the body of OHCs are in
direct contact with the cochlear fluids, as we would expect a pressure detector
to be. Moreover, as we go from base to apex, the OHCs show a steady gradation in
length: the OHCs are tuned (and examination of OHCs in vivo has shown
this tuning explicitly).

Of course, this tuning is not as sharp as we observe SOAEs: less than 1
Hzin some cases. Here is where positive feedback comes in, and I have
posited that reverberation arises between triplets of OHCs via ripples generated
on the tectorial membrane (in which the stereocilia are embedded), since it is
known that stimulation of the OHC causes movement of the stereocilia, as well as
the reverse. The attraction of this concept is that it makes use of the
properties of a reversible transducer, explains why OHCs occur in triplets in a
quasi-crystalline arrangement, and, in addition, gives a prominent role to that
much overlooked structure, the tectorial membrane (TM). The peculiar elastic
properties of this gelatinous body are here called on to support
slow-propagating ripples. It is therefore important that the stereocilia are
embedded in the membrane so that movement of the stereocilia can generate
ripples.

I have hypothesised ripples because they are
isotropic, and the surface of the TM appears to be covered with an amorphous
substance. This arrangement fits in with
my measurements of the OHC 'crystal lattice' whereby the L1 resonator
(relative length 1.06) sits well placed with respect to the other
resonators to produce musically significant ratios (particularly the L5
resonator at length 2.0). Of course, other wave propagation modes within the TM
are possible; Rayleigh waves are one example, but it is not clear that the TM
properties would be such as to give a Rayleigh wave with a sufficiently low
wave propagation speed to tune the three rows of OHCs to a whole wavelength. By
contrast, surface-tension borne ripples are known to already have, on water, a
low propagation speed (30-40 mm/sec), and it would be expected that the
corresponding speed on the interface of a gel immersed in water would be even
lower.

My hypothesis has shown up a lack of physical
data on the TM, but in offering a hypothesis that can be tested, my hope is that
hearing science will be advanced. I have suggested a transverse wave propagating
in a radial direction, and I am not sure if your hypothesis calls for a
longitudinal wave propagating in the radial direction, or something else. I am
happy to entertain a longitudinal wave propagation mode if its speed can be made
sufficiently low to tune the cavity to a whole wavelength. The presence of
fibres within the TM opens up the possibility of many different propagation
modes. However, it seems to me that capillary waves (ripples) present the
simplest mechanism with which to get the hypothesis off the ground.

I will
finish here for now. My answers to your individual queries are
interspersed between your text
below.

At this point, I wish to thank you for your
constructive comments. I believe that a resonance theory of some sort is
the only way to answer the requirements of the ear's high Q (as so
perceptively demonstrated by Gold and Pumphrey). The hypothesis that I have
proposed is able to fulfil that requirement; it is also able to explain most of
the hearing phenomena that I know of. As a person trained in physics, I
wanted to present a 'big picture' perspective based on fundamental physical
principles that would give a satisfying synthesis of how the ear works. For that
reason, it potentially covers the whole of the field (a lot for a single paper),
and naturally some areas will not be covered in enough detail to satisfy
everyone. Nevertheless, I hope this theory points in the right direction and
suggests some worthwhile modeling and experiment.

I very much agree with some important
ideas you outlined in your intriguingpaper on the underwater piano.In
particular we share the opinion that the traveling wave is just
anepiphenomenon, but most likely the stereocilia of the outer hair cells
actas the primary sensory elements.

------snip-------

how can the stereocilia resonate to acoustic
energy?

-----snip------

I would merely
recommend to not ignore the work of Hudspeth who has shownthat
depolarization of the hair cells coincides with opening of ionchannels at
surface of the stereocilia. Kiang and more recently Ruggerogave evidence for
immediate response to rarefaction whereas response tocondensation is delayed
by half a period. So it would possibly be somewhatmisleading to understand
OHCs as reacting to over-pressure.

----snip-----

I am not denying that something happens at the tips of
stereocilia. I am

simply seeing OHC as reversible transducers. When the
body of the OHC

is stimulated by
acoustic pressure, that causes the stereocilia to bend;

conversely, when the
stereocilia are bent, that causes the body of the OHC

to respond (see
below).

----snip-----

What about your
suggestions of reverberation between adjacent rows of haircells, resonant
cavities like a laser cavity, etc. I would need much moreprecise
descriptions in order to be able and follow you. Surface acousticwaves seems
to me more realistic, in principle.

----snip-----

These are both
analogies of the reverberation process that I envisage.

Both have a wave
propagating from one end of a cavity to the other,

where it
is
reflected; the process is repeated and the wave is amplified,

resulting
in an
active resonant cavity with coherent wave energy

emerging
at the end.
If you have problems with the term 'acoustic

laser', then it
might be better to keep to the analogy with the surface

acoustic
wave
resonator, which seems closer to what is happening in

the cochlea. To
recapitulate, the body of the OHC detects sound

energy and causes
its stereocilia to move, launching a ripple in the

TM. When the ripple
encounters a neighbouring OHC, its

stereocilia are
bent, depolarising the cell and causing the body of

the cell to react.
The vital amplifiying mechanism at work is that
the

OHC endeavours to
return itself to its resting membrane potential.

The stereocilia
therefore 'kick back', returning to their original

undeflected position
faster than they were deflected away from it,

in the process
consuming cellular energy and amplifying the

amplitude of the
ripple. The ripple returns to the OHC where it

began, and the
process repeats. It may help to imagine the

stereocilia
'connected' to a molecular motor in the OHC's

cytoskeletal spring:
when the stereocilia bend in one direction

(away from the basal
body, for example) they cause the spring to

contract,
and when
the stereocilia bend in the other direction,

toward the basal
body, the spring expands. An active servo

mechanism, a
molecular motor of some sort, is continually at

work returning the
spring to its resting position.

----snip-----

However, why did not youdeal with alternative radial
oscillations, being already substantiated bymeasurements which were
published in several abstracts of previous AROconferences?----snip-----

As mentioned above, I am happy to entertain radial
oscillations

if they are able to give a sufficiently low propagation
speed that

the cavity is
tuned to a whole wavelength.

----snip-----

How do you
interpret that the tips of the stereocila of the OHCs areobviously embedded
in the tectorial membrane? I refer to N. Slepecky(1997), "Anatomy of the
cochlea and auditory nerve", chapter 107 inEncyclopedia of Acoustics, p.
1350, Fig. 4.

----snip-----

The attachment is necessary so that the stereocilia can
launch

a
ripple in the TM when they move in response to
acoustic

stimulation of the OHC
body.

----snip-----

If neural fibers are able to rapidly convey ions, why not
expect the sameinside TM? Because I am qualified an electrical engineer, I
tend to makessuch exotic conjectures first.

----snip-----

You seem to be suggesting that the stereocilia convey
charges to

the TM. Can you describe what happens next and how the
IHC

finally respond?

----snip-----

Do
not take me wrong, I would like to stress and acknowledge once againthat you
pointed the list to the need for a serious revision of the presentdoctrine.
Even if the majority might have more problems than me with yourwhole paper,
I strongly support the publication of what I consider the verypoint, i.e.
prominent radial resonance. This holds on condition you areready to
rigorously purify your reasoning from any speculative orinappropriate stuff,
no matter whether or not your models on lattice andmusical ratio could be
correct.